MATHEMATICAL KNOWLEDGE FOR TEACHING-2 Adnan Baki Karadeniz Technical University

2 Shulman’s and his followers’ categorisation for teacher knowledge:

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7 From this literature we divided teacher knowledge into three categories: content knowledge, pedagogical content knowledge and curricular knowledge. From this literature we divided teacher knowledge into three categories: content knowledge, pedagogical content knowledge and curricular knowledge. Today we are going to specify teaching knowledge associeted with CK and PCK Today we are going to specify teaching knowledge associeted with CK and PCK

8 CK+KC+PK+PCK = TK Content knowledge is the only one necessary for effective teaching? Content knowledge is the only one necessary for effective teaching? OR OR Pedagogical content knowledge is the only one for effective teaching? Pedagogical content knowledge is the only one for effective teaching? Traditionally most of us believe that “you don’t know a subject until you have taught it” Traditionally most of us believe that “you don’t know a subject until you have taught it” This view implies that teacher first should know subject to be able to teach. This view implies that teacher first should know subject to be able to teach.

9 Of course this is true at the beginning. There is seemingly no any problem for this conception of teacher role and the importance of content knowledge. Of course this is true at the beginning. There is seemingly no any problem for this conception of teacher role and the importance of content knowledge. But there is a hidden ganger in this belief or conception that ignore the role of pedagogical content knowledge as one of the main components of knowledge for effective teaching. But there is a hidden ganger in this belief or conception that ignore the role of pedagogical content knowledge as one of the main components of knowledge for effective teaching. As we have seen the schematic explanations in the literature there are different classification for teacher knowledge. There is no agreement between them. As we have seen the schematic explanations in the literature there are different classification for teacher knowledge. There is no agreement between them.

10 CK Knowlwdge of Curriculums KTPK PCK Beliefs The network of PCK in Shulman, Grosman, Ball, Franke, Shuhua An

11 Usually CK, PK, TK and beliefs are seen as components of PCK. Usually CK, PK, TK and beliefs are seen as components of PCK. Related literature usually shows TK as a core component of PCK. Related literature usually shows TK as a core component of PCK. I have an objection to this interpretation. I have an objection to this interpretation. If the final target is to operate an effective teaching and promote student’s learning, then we have to ask which one is the first and which one cover the other? If the final target is to operate an effective teaching and promote student’s learning, then we have to ask which one is the first and which one cover the other? TK should play the central role in teacher’s knowledge. TK should play the central role in teacher’s knowledge. To me CK, PK and PCK are the component of TK. To me CK, PK and PCK are the component of TK.

12 BeliefsCK Knowlwdge of Curriculums PCKPKKT The network of Knowledge of Teaching in Baki About; the nature of math; learning teaching learner teacher

13 Knowledge of content consists of broad mathematics knowledge as well as specific mathematics content knowledge at the grade level being taught. Knowledge of curriculum consists of the awareness of the content, goals, expectations, approaches and key ideas of the particular curriculum. It requires a full understanding of the objectives, concepts and skills stated in the curriculum. It also requires the abilty to select and use sitable curriculum materials.

14 Knowledge of pedagogy consists of teaching procedures, effective strategies, planning, menagemnet techniques and motivational techniques. It requires; to know specific methods for making subject learnable;to know specific methods for making subject learnable; to know how guide students to improve their understanding;to know how guide students to improve their understanding; to know how facilitate discussions to help knowledge construction.to know how facilitate discussions to help knowledge construction.

15 Pedagogical content knowledge consists of the knowledge of content and pedagogy. It requires to know specific representations, examples, applications of the content. Pedagogical content knowledge consists of the knowledge of content and pedagogy. It requires to know specific representations, examples, applications of the content. It requires to know what kind of background students come from. It requires to design the particular lesson choosing the spesific methods suitable for teaching the particular content. It requires to know what kind of background students come from. It requires to design the particular lesson choosing the spesific methods suitable for teaching the particular content. It also requires to know how to prepare a good scenario by using a rich teaching repertoire. It also requires to know how to prepare a good scenario by using a rich teaching repertoire.

16 Knowledge of teaching (as an action performing the scenario) consists of CK, KC, PK, PCK and beliefs. It requires to know studets’ thinking, understanding and learning. Knowledge of teaching (as an action performing the scenario) consists of CK, KC, PK, PCK and beliefs. It requires to know studets’ thinking, understanding and learning. It requres to know how to organize instruction (planning and implementing). It requires to have mastery of modes of delivering the instruction. It requres to know how to organize instruction (planning and implementing). It requires to have mastery of modes of delivering the instruction.

17 An example of the components of teaching knowledge: An example of the components of teaching knowledge: Imagine that a teacher intented to allow students to discover the patterns for themselves. Imagine that a teacher intented to allow students to discover the patterns for themselves. The structure of the lesson itself as a guided discovery is a pedagogical decision. Therefore it includes knowledge of pedagogy. The structure of the lesson itself as a guided discovery is a pedagogical decision. Therefore it includes knowledge of pedagogy.

18 The decision about how to lead students to recognize relationships in a particular subject matter requires curriculum knowledge and petagogical content knowledge. The decision about how to lead students to recognize relationships in a particular subject matter requires curriculum knowledge and petagogical content knowledge. The decision about what kind of questions to ask to help students to develop their understanding requires knowledge of pedagogy and PCK. The decision about what kind of questions to ask to help students to develop their understanding requires knowledge of pedagogy and PCK. The decision about to use a particular activity requires PCK The decision about to use a particular activity requires PCK

19 KUVVET ÖĞRENCİNİN CEVAPLARI The teacher knows that a 0 = 0. This is content knowledeg One of his students’ respond is 2 0 = 0. When teacher asks why you are thinking that way? Then suppose that student explains this…x 4 = x.x.x.x, so there are four x, similarly 2 2 = 2.2, there are two 2. To know how teacher react and respond this situation is PCK. In this case knowledge of teaching is more than this. Knowledge of teaching requires to choose and use suitable representations to make effective explanation and to give counter example to remediate misconception.

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